Dating myself. I too was a Engineering and Wharton grad...20 years ago. Yeesh.
I found my way into a Product Management internship in 1994 by luck and happenstance. The honest assessment of the recruiter was "you are too technical for marketing, and not technical enough to test or write code."
There's some truth to that.
As someone who has been in product management my entire career, in my own VC funded startup, MSFT, AMZN, now ORCL (was part of a small company ORCL bought), spanning HW and SW, Cloud, and mobile phones, enterprise and consumer, I posit the following from my own personal experience.
I try to simplify things to make it easy for people to understand. Product managers need to worry about "the what, and the why, and sometimes the how". In smaller companies, where they are also managing scrums, etc, they can focus on the "when" but as companies grow, and more specialized program managers exist, or engineering leaders are more actively engaged in this part of the product lifecycle, they can worry about this less.
It irks me when I meet product managers who haven't written code, or don't try to prototype things. Ideas are cheap. I am not a great coder. I joke that me and code is like a kid and a hand grenade. At first glance it's cute, but it will get messy when the thing explodes. The best way to improve on a SW based idea is to show a hacker/developer crappy code. They can't help themselves but to try and improve it. Selling the vision has as much to do with the idea as it does with your ability to empathize with the customer need and pull together something into a cohesive thing that can be touched. Code always wins.
Your job, as the product manager, is to shepherd the idea/vision through to completion. That vision must be viable. You must not be in love with your idea. You must be in love with solving a customer problem. Engineers sometimes get stuck on the solve. Great product managers focus on the problem, and refine it with simplicity.
If you cannot answer "what" and "why" you are not doing your job.